Letting $f:[0,1]\rightarrow\mathbb{R}$ be measurable, and letting $F(x,y) = f(x)-f(y)$, is $F$ necessarily measurable?
2026-03-30 18:11:53.1774894313
Measurable Function on Product Space
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$F_1(x,y)=f(x)$ and $F_2(x,y)=f(y)$ are measurable (Can you verify this?). Hence $F=F_1-F_2$ is measurable.